The single‐layer problem in the atmosphere and the height‐integral of pressure

(1) The conditions under which the atmosphere could be treated as a single dynamical layer are investigated theoretically. (2) We have found nothing in the observations to justify the hope that the atmosphere could be treated as a single dynamical layer. Some possibilities, however, remain unexplored. (3) P i , the height‐integral of pressure, has been computed from the published records of registering balloons. The termini 1 of the integral have been 500 metres above mean sea‐level, and a height so great that the air above it is negligible. (4) The value of P i , found from the mean distribution, is 7.1 × 10 11 dyne cm. −1 at the equator, and 6.9 × 10 11 in latitude 50° N. (5) When balloon ascents are taken individually, P i at European stations ranges from 6.5 to 7.2 bar km. (6) When many ascents are considered at one place, the variations of P i are correlated with those of p i . For the winter season the points on the ( p i , P i ) diagram lie near lines having the slope dP i / dp i =12.4 km. for Lindenberg (long. 14° 7′ E, lat. 52° 13′ N), and 8.1 km. for Pyrton Hill (long. 1° 6′ W, lat. 51° 42′ N). For other seasons the scatter is large. The name “temporal dynamic height” has been given to dP i / dP i found from many times at one place. (7) When two places are compared at one time the ratio of the difference of P i to that of p i has been called the “ spatial dynamic height,” and denoted by J. The median value of J is found to be 9.90 km.; but J varies from −50 km. to + 80 km. (8) Because these two dynamic heights are so unequal and inconstant it follows that Laplace's equations for free tidal oscillations in an ocean of uniform depth are a very bad description of ordinary disturbances of the European atmosphere. We have not examined the question whether the same equations, modified by additional terms to represent the gravitational field of the sun and moon, are a good description of small special forced tidal oscillations of the atmosphere. (9) In particular we need no longer be puzzled by that conflict between tidal theory and observation which provoked this research, namely, that when the free tidal equations are applied to an atmosphere above a horizontal earth they imply that the surface pressure p G is rising wherever p G , increases towards the east. 2 This refers to the tidal equations in their usual form, in which terms of the second degree in the velocities are neglected. Dr. Jeffreys has shown that the second‐degree terms may have important effects. 3 . (10) The variations of J have been explored in a number of ways, but no simple connections have been found. (11) Equations sufficient to predict the changes of pressure, density and momenta are formulated in š 5 for a dry atmosphere moving adiabatically. But these equations cannot be summarized for a “single layer.”.